Normal Transformer / LC Tank Damping
Load Lines with Load Line Spread Sheet

The plots start at 1 Hz. This is useful for seeing trends below 20 Hz, but what we normally care about is what is happening at 20 Hz and higher.

The plots stop at 1000 Hz. The model we are using isn't valid above 1000 Hz because it does not include parasitic capacitances and leakage inductance.

Here is a simplified model of a Parafeed circuit. The DCRs of the plate choke and transformer are omitted and the impedance of the B+ is set to zero.  Because the losses in the iron and copper are not included in the model, when we see resonances, they will be are larger than in real life.

Here is a basic frequency sweep with a huge 40,000 Henry plate choke. This is equivalent to a CCS feeding the tube instead of a plate choke.

• The top trace is the output of the amplifier in dB.
  
• Generally the flatter the better.
  
• Gentle slopes as we go below 20 Hz towards 1 Hz are usually better than steep slopes down. 
  
• Note that the difference between a -3 dB point at 20 Hz and 22 Hz is probably not audible.
  
• Remember, keep an eye on  the big picture.

• The bottom trace [(V(Plate)/I(V1))] is the plate load impedance as seen by the tube.
  
• The higher is better if the phase angle is at zero degrees.
  
• If the phase angle is not zero, higher impedance is still better, but 5K at zero degrees is usually better than about 6K at 45 degrees.
  

• The middle traces are the phase angle of load impedance seen by the tube (green) [P(-V(Plate)/I(V1))] and the phase angle of the voltage at the output (red)  [P(V(Primary))].

Now lets drop the plate choke down to an affordable 40H. My normal rule of thumb for a plate choke is it should be 8H for every kohm of load or larger. So with a 5K load, the plate choke should be about 40H or more.  Other people use 10H per kohm of load as a rule of thumb. The difference between 40 and 50H isn't that big. We normally don't care about the phase shift at 20 Hz to the speaker (red trace in middle plot), but it is included in this plot anyway.

The running of plots one at a time makes it difficult to see what is changing. So what I'll do next is sweep one parameter at a time (plate choke, Parafeed cap and primary inductance) so we can see what each parameter does.

Lets run plots with the Parafeed cap set to 0.2 uF, 2 uF, 20 uF  and 200 uF. For clarity, I deleted the phase at the load (the speaker). We care more about the phase angle of the plate load seen by the tube than the low frequency phase at the speaker. We can see more capacitance leads to a lower - 3 dB frequency (good), a flatter phase angle on the load line (good) but a lower impedance load line (not so good if it occurs in the audio range.)

--- There are two other things we care about in an audio amp. ---

There are at least two other things we care about in an audio amp. The top two things that come to mind are the power supply ripple rejection and output impedance (damping factor).

• The power supply rejection is run with the load attached to the amplifier.
• -40 dB is better than -30 dB for the power supply rejection. However, I doubt anyone could hear the difference between -40 dB and -37 dB at low frequencies. The top set of curves is the power supply rejection in dB, more negative (lower) is better.
• Note: Yes I know rejection should be specified as a positive number, but the plots are easier as a positive number.
• -40 dB means 1V of ripple on B+ is reduced to 0.01V a the primary of the transformer.
  
• There is a question to be resolved: Display actual power supply ripple rejection  or display ripple rejection divided by small signal output response. This isn't signal to noise because noise involves more sources than just the power supply, but  it is similar. The advantage of this is it is harder to fool ourselves that we've improved the PSRR with out hurting anything else.

• The output impedance of the amplifier is usually measured with the load removed from the output of the amplifier. 
• This will remove any damping the speaker provides for the amp; however, we want the amp to damp the speaker, not the other way around. 
• The bottom trace is the impedance at the output of the amp (lower is better) with the reflected transformer load impedance removed from the equation  with different Parafeed capacitors.
  
• The peaks in real life won't be that high because of losses in the iron, but the trend will be the same.
  
• Lower Parafeed capacitor values leads to higher output impedances (lower damping factors.)

For both curves: Lower is better, flat is better.
First  lets look at the results displayed as Power Supply Rejection and Output impedance.


Now lets decide how we want to display rejection of B+ ripple, PSRR. Lets examine the plot below to see what we learn.

• The bottom plot is PSRR displayed as how much ripple from B+ actually makes it to the output.
• 0.2 uF looks impressive compared to all the other values. However, remember: There Ain't No Such Thing As a Free Lunch. (TANSTAFL)
  
• The middle trace is how much voltage swing from the tube actually makes it to the output.
• Notice that 0.2 uF rolls the output off at a fairly high frequency. This is one "Bills" we pay for a "good PSRR lunch". The question is did we get what we paid for?
  
• The top trace is the bottom trace divided by the middle trace.
  
• This normalizes the voltage on the output from the power supply to the voltage on the output from the tube. This allows us to make a better comparison of what the changes do.
• Looking at the top plot, we see that changing the Parafeed capacitor value doesn't affect the PSRR when it is normalized to the output response.
• Digging deeper, this means for dB we gain in B+ ripple rejection we lose a dB in audio output.
• In other words  for every dB in rejection we get we loose a dB of music.
  

In general,

• Zout (damping) is better with large Parafeed capacitors.
• -3 dB at the output is better with large Parafeed capacitors
• The load line (impedance seen by the tube) is best (to my eyes) with a medium Parafeed capacitor. A small Parafeed capacitor gives the highest load impedance, but the phase angle [ P(-V(plate)/I(V2) ]is not resistive so the load line becomes elliptical.
• A small Parafeed cap gives better power supply rejection at low frequencies, BUT, this rejection is at the expense of a higher - 3 dB point and a worst damping factor. I'd stick with medium to large Parafeed capacitors.

Overall, I'd start a design with a moderate Parafeed cap: 8 uF / 1K of plate resistance (1K = 8 uF, 2k = 4 uF). More capacitance will give better damping. A lower value will roll off the -3 dB point so as to not drive the Parafeed transformer as hard if saturation is a problem. If I wanted to raise the -3 dB point (say from 20 Hz to 40 Hz), my preference would be to use the large Parafeed capacitor for good damping and roll the -3 dB point off in the drive to the output stage .

Let's  examine what happens with the plate choke at 4H, 40H and 400H with the Parafeed cap (Cpara) set to 2 uF and then to 20 uF. 

• On the top plot (VdB(Primary)) we want to see a low - 3dB frequency without peaking.
• The bottom trace [(V(Plate)/I(V1))] is the plate load impedance as seen by the tube. We want this to dip down at as low a frequency as possible.
• The middle plot is the phase angle of the the plate load impedance. We'd like this to be zero degrees to as low a frequency as possible.
  

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Here's the power supply rejection (top) output impedance (bottom) with the plate choke at 4H, 40H and 400H.
For both curves: Lower is better, flat is better

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Here's one where the PSRR isn't normalized. When it is normalized, it is easy to see that at 4H, the power supply noise is higher than the music below about  80 Hz. When it isn't normalized to the output response, we completely miss this wonderful discovery.

In general,

• Zout (damping) can be better with smaller plate chokes (4H).
• -3 dB is better with large plate chokes (400H)
• The load line (impedance seen by the tube) is best with a large plate chokes (400H).
• The Power Supply rejection is greatly influenced by the plate choke and more inductance is better.

Let's examine what happens with the primary inductance of the transformer at 4H, 40H and 400H with the Parafeed cap (Cpara) set to 2 uF and then to 20 uF. 

• On the top plot (VdB(Primary)) we want to see a low - 3dB frequency without significant peaking.
• The bottom trace [(V(Plate)/I(V1))] is the plate load impedance as seen by the tube.
  
• We want this to dip down at as low a frequency as possible.
• Upward peaks are acceptable if the phase angle stays close to zero.
  
• The middle plot is the phase angle of the the plate load impedance. We'd like this to be zero degrees to as low a frequency as possible.

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Now for the PSRR and output impedance.

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I've been told that most good Parafeed Transformers will run 50H of primary inductance per kohm of rated primary impedance. This means a 5K primary should run around 250H.

• Large Parafeed Primary inductances are good in just about all ways we've looked at.
• The correct way to get large primary inductances is through careful manufacturing and good materials
• Adding lots of  primary turns on the same core to get a large primary inductance adds insertion loss (DCR) and leakage inductance (which makes the upper -3 dB point worse.)
• >40H per kohm of reflected load is a good starting point for power amps.
• The Parafeed Primary inductance does not have any useful effect on the B+ ripple rejection.
• A small primary inductance will attenuate the B+ ripple, but for every dB it attenuates the B+, it also attenuate the audio.
• A low primary inductance improves the output impedance of the amp, at the expense of a harder load line to drive (better damping for higher distortion.)
• There may be some argument that since the output impedance of the amp is inductive, not resistive, it doesn't help the damping as much as it should.
  

Part 1.4
Summary of  what we learned with the simple model

• Plate Choke
• Below 1 kHz, you can't make the plate choke too large. Economics of weight and cost will limit the size of the plate choke.
• The plate choke is the only good place to get more power supply ripple rejection with a given output tube.
  
• 10H per kohm of reflected load is a good starting point for power amps.
• 40H per kohm of plate resistance is a good starting point for driver stages and preamps.
  
• Remembering TANSTAFL
  
• As the plate choke gets larger, the DCR will usually increase leading to a higher B+
• As the plate choke gets larger, the capacitance CAN increase which will hurt the performance above 1 kHz
• As the plate choke gets larger, it is more likely to couple to other parts.

• Parafeed Capacitor
• A small Parafeed capacitor can be used to raise the lower -3 dB point to a higher frequency.
• Why raise the -3 dB point? Raising the -3 dB point helps keep subsonics from robbing available output power (saturating) of the Parafeed transformer.
• If you want to limit the -3 dB point, I recommend limiting it in the driver stage, not with the Parafeed capacitor.
• A small Parafeed capacitor can reduce the coupling of B+ noise, but this has a high performance cost in that it worsens the damping factor and increases the -3 dB frequency.
  
• For every dB of B+ noise you reject with a small Parafeed cap, you lose 1 dB of signal.
• A small Parafeed capacitor hurts the damping factor. A large Parafeed capacitor helps the damping factor.
• The load line is best with a moderate (tuned) Parafeed capacitor.
• Starting from scratch, I'd pick the Parafeed capacitor for a flat damping factor above 20 to 40 Hz or so.
  
• To set the Parafeed capacitor equal to the plate resistance at 20 Hz (the limiting factor for damping factor), use a capacitor that is 8 uF / 1K of plate resistance (1K = 8 uF, 2k = 4 uF). I'd use this rule for power amps and preamps. I haven't decided if I'd use a smaller cap in a driver stage or not.
  
• Start with a cheap capacitor and voice your amp's bass, then buy a good film and foil capacitor (oil optional)
• Don't be afraid to experiment with the Parafeed capacitor value.

• Primary Inductance
• Higher is better in most cases.
• A smaller value used as a grid choke in a driver stage has the advantage of recovering faster when the grid of the output tube is driven positive.
• A smaller value can be tuned for better damping, but at the expense of changes in the load line and in the lower - 3 dB frequency response.
• If using a smaller Primary inductance, you'll definitely want to play with tuning the Parafeed capacitor.
  
• >40H per kohm of RATED reflected load is a good starting point for power amps.
  
• You usually don't have much say in this parameter except to order premium core materials.

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Part 2

Let's add a few losses to the simple model

Lets add the DCR (DC resistance) of the choke and the DCR of the transformer to the model. These parasitics are easy to measure, calculate and understand. The core loss isn't easy to measure and most manufacturer's won't give it to you.

• DCR of the choke is fairly straight forward. It adds a voltage drop from the DC bias of the tube.
  

• The DCR of the transformer adds insertion loss to the transformer.
• This means if we put one watt in the input, we get less than one watt on the output.
• There are several ways transformer manufactures deal with the losses from the DCR.
• The turns are set to the ideal turns ratio. Both the reflected primary impedance and the output voltage will be off.
• The turns are compensated so the loaded output voltage is correct (this is usually done on power transformers.)
• The turns are compensated so the loaded primary impedance is correct (some audio transformers.)
• A combination of the above.
• I'm using an impedance compensated model for the transformer (the primary impedance is correct.)

Sweeping the plate choke at 4H, 40H and 400H, we get an output response that looks like the following. It is kind of hard to tell the difference between the two except that the output is about a dB lower.

Subtracting the two outputs gives us a magnified view of what is changing.
The top plot shows that the DCR of the plate choke adds a bit more power supply rejection when the plate choke is small (4H).
The bottom plot shows the DCR of the transformer adds 1 dB of loss at 1 kHz. The DCR of the choke adds some voltage gain at subsonic frequencies.

The effects of the DCR on the output impedance can be see in the following plot. At 1 kHz, the DCR of the transformer makes the damping factor 1.26 times worse.


The output impedance of the amplifier is dominated by the plate resistance of the tube followed by the resistance of the transformer windings. If you want better damping in a SET or Parafeed amp with a given tube, you have to give up some output power and use a higher primary impedance on the transformer. A 10K primary should have two times better damping than a 5K and a 5K should be twice as good as a 2.5K. Remember TANSTAFL? To get the better damping we give up something. If 2.5K is the resistance needed for maximum power out, the 5K and 10K will give progressively lower output power for the same tube and bias point.

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Part 3

DrP, Damped Resonance Parafeed
It's more than an excellent soft drink.

(Plots and long diatribe to be added later)

With good iron in a Parafeed power amp, DrP doesn't help too much. You can some times use it to tweak a bit more low frequency power out.

If we use budget iron, Damped Resonance Parafeed adds some additional parameters we can tweak to trade off power handling vs damping vs -3dB points.

In a driver stage or preamp, DrP can greatly reduce the low frequency resonance of the unloaded Parafeed tank without having to add a resistor across the grid choke or Parafeed transformer to ground. This is good because it gets us a little more voltage gain out of the circuit and greatly reduced the loading on the tube (which makes the tube sound better in my book.)

Because of the DrP resistor in series with the DrP capacitor, the Parafeed capacitor shorts out the "sound" of the DrP cap at almost all frequencies. This means the DrP cap can be a slightly lower grade than the Parafeed capacitor. I happen to like metal foil capacitors. DrP means I could use a metal foil (film and foil) capacitor for the Parafeed capacitor and then use a metalized cap for the DrP cap.

Click on this link for technical discussions on Transformer / LC Tank Damping

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Part 4

A Spread Sheet to Play With

To use this spread sheet, you'll need to have your EXCEL install disk in hand and do the following:

    In Excel, Click on
        Tools
          Add-ins
             Analysis ToolPak      [not the Analysis ToolPak - VBA]
                Put your Excel install disk in the CD drive and follow the rest of the instructions.

Click here to get the Excel File: Parafeed Circuit Spread Sheet

The Excel spread sheet models this circuit from about 1 Hz to 1 kHz.


The data section of spread sheet looks something like this:

The spread sheet will model two designs at once so you can compare them.
INPUTS

• All inputs are in cells with a YELLOW back ground.
• The Rplate of the tube and Rload are the easy numbers to pick. If you don't know what the numbers are, just used the suggested "Typical Starting Values"
• If you don't want to use DrP, just set the C_DrP = 1% of the actual Parafeed capacitor and the R_DrP= 0.
• To make this a CCS fed Parafeed, Set the R_Choke_DCR to 1,000,000
  

Outputs
The normal things we care about are listed in a table format

• The Output Peaking is the highest peak from 1 Hz to 1 kHz with respect to the 1 kHz output level to the speaker.
• The -3 dB Small signal frequency is the calculated -3 dB  low level response assuming the inductance of all the magnetics does not change with drive or frequency.
• The - 3 dB power response is where the load on the tube drops to 70% of the 1 kHz load. On preamps and grid choke designs, this number will have no meaning. On a tube with a load impedance set to maximum power output, this number is the frequency where the distortion starts to rapidly climb.
• PSRR at 100 Hz and 120 Hz is how much the Parafeed design attenuates the B+ ripple at 100 Hz and 120 Hz.
  

Spot Frequency Check

Cell K3 (30 Hz) lets you input a frequency for a detailed analysis. You can enter any frequency you want between 1 Hz and above 1 kHz.

One thing that is missing is an analysis of the transformer saturation limited allowed output power vs frequency. I'm not sure this is a big deal to not have it.

1. I'm not sure if we can get consistent data from the transformer manufacturer's that is taken at the same level of peak distortion, input loading, output loading etc.
2. I'm not sure if anyone other the Paul Joppa could use that curve without messing up all the other parameters.

The "normalized" load impedance seen by the tube vs frequency plot looks like the following.


The small signal frequency response and power supply rejection is given in a plot that looks like the following. For dB out, flat and a low - 3dB is best. For PSRR, in this plot more negative is better (-50 is better than -40). If you look close, you'll see the 1 kHz Vout is not 0 dB. This is because the plot shows the effects of loading on the tube.

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Part 4.1
Lets Examine a Driver Stage.

• CCS fed plate  
  
• Set R_Choke_DCR to 990k
  
• 1000 times R_plate is also a good way to change to a CCS drive
  
• .33 uF Parafeed cap
• 750H 900 grid choke with no parallel resistor [ Note: Set R_load to 990K or 1 meg ]
• 7000 ohm Rplate

We see that the output peaking (Design 1) is 13.4 dB and if we increase the capacitance by adding the DrP cap with no series resistance, the peaking is 11.2 dB. This is a hint that just adding more capacitance won't kill the peaking easily.


Lets add the estimated value for R DrP and see that the peaking drops from 11.2 dB down to 5.32 dB.

Just for kicks, we'll use the Excel Goal seek function to try to drive the peaking down.

Goal Seek function is found under

TOOLS
    Goal SEEK

The trick to using goal seek is not to get greedy all at once. Don't go for zero on peaking. Go for a little smaller than the existing peaking. If it doesn't work, try a different goal and it may work. In this case, the goal seek couldn't find a better value than the estimated value.

With a 0.33 uF DrP, the output response's improvement can be seen in the following plot.

DrP works better with the DrP cap set to 2 to 3 times the Parafeed capacitor. Using the suggested DrP resistor, 2X cap has 3.19 dB peaking where 1X had 5.32 dB peaking. After running the goal seek optimization, the 2X gets 0.01 dB better. Not that big of a deal. This also shows that the DrP resistor isn't very sensitive to its value. We changed it 10% and got almost no change.


Lets check a 1 uF DrP. Going from 2X to 3X buys us 1 dB less peaking. For 1 dB I'd just use the 2X value.


The historical way to kill the subsonic peaking in a driver is to put a resistor across the grid choke. This kills the peaking, but it makes the driver tube work harder. Lets use Goal seek to pick a damping resistor across the grid choke and compare it to a 2X DrP damping cap. Remember to use small steps when tweaking in the peaking by changing part values with goal seek.

To get "0 dB" peaking we need to put a 36K resistor across the grid choke. 

At 1 kHz, the grid resistor costs us 1.5 dB in gain over adding the DrP cap.

Now for the interesting plot.

• The load the driver needs to drive is about 501K at 1 kHz using DrP
• The load the driver needs to drive is about 34K at 1 kHz using the damping resistor across the grid choke.
• At 40 Hz, DrP presents a 166K load to the tube and the resistor across the grid choke presents a 34K load.

I'd much rather have the 166K load on the tube than the 34K load on the driver tube.


Now to be fair to the Resistor across the grid choke damping method. Lets increase the resistor across the grid choke until the load at 40 Hz is 166K. This requires using a 1.09 megohm resistor across the grid choke. The peaking is now 13.6 dB with the resistor across the grid choke instead of 3.2 dB with the 2X DrP configuration.


Like I said, DrP. . . it's more than an excellent soft drink.
Here's the before and after schematic. Note: R4 and R8 aren't real resistors in the circuit.

Here's the DrP plots. The output peaking is slightly different than the Excel spread sheet mostly because the Pspice plot uses fine frequency steps and the Excel plot uses course frequency steps.

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Part 4.1.1

Is This Gain Peaking a Problem?.

 
Lets not lose track of the ball:

• Take all measurements with a grain of salt. We are talking tubes here. If measurements meant something actually sounded better, we'd be listening to Solid State.
  
• Measurements are good for helping us make decisions instead of guesses. Measurements won't tell us how it sounds, but they can help us understand what we need to change to improve the sound. This is as long as we don't mess anything else up in the process and we're smart enough to make the "right" measurements.
  

Thoughts on 1-20 Hz gain peaking issues:

• Because the “5 Hz” gain peaking can be excited by B+ and grid conduction, rolling off the gain of previous stages does not completely remove the risk of having problems.
• 1-20 Hz is a problem area with LPs. Subsonics from a record can aggravate low frequency gain peaking.
  
• 1-20 Hz could be a problem with bias recovery from repetitive clipping (either at the drive tube or forward biasing the grid of a tube on the output of the Parafeed stage.) Asymmetrical clipping is usually worse than symmetrical clipping.
• 1-20 Hz can be a problem with 115V line modulation. I've seen a 3 Hz B+ ripple in my equipment I can't explain. Line dips and peaks could cause large excursions in the bias point. Plug a 500W lamp in to the same outlet as the amp to check for problems when the lamp is turned on and off.
• 1-20 Hz could be a problem with motor boating between tube stages that share a power transformer.
• IF there are more than one gain stage in a system, make sure that if there is peaking, that the peaking does not occur at the same frequency. Three 15 dB peaks at 5 Hz gives a total system peak of 45 dB. With multiple stages and amps, either split the frequencies where the peaks occur an octave apart or damp the peaking some how.
  

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Play safe and have fun out there.
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